1. Suppose we measure b at times t= -3,-2, -1,0, 1,2, 3 and we obtain the...

Transcribed Image Text:

1. Suppose we measure b at times t= -3,-2, -1,0, 1,2, 3 and we obtain the vector [0,0,0,1,0,0,0], (a) To fit these 7 measurements by a straight line C + Dt, what 7 equations would we want to solve? Write these equations as Ax=b and identify A, x, and b. (b) Can you solve Ax=b? Justify your answer. (c) Formulate a least squares problem for this data fitting problem. How is the solution of the least squares problem related to x? Illustrate the idea via a graph. (d) Solve the least squares problem for the approximate (best) solution x. Show also the solution graphically. (e) What is the projection p of the vector b onto the column space of A? 1. Suppose we measure b at times t= -3,-2, -1,0, 1,2, 3 and we obtain the vector [0,0,0,1,0,0,0], (a) To fit these 7 measurements by a straight line C + Dt, what 7 equations would we want to solve? Write these equations as Ax=b and identify A, x, and b. (b) Can you solve Ax=b? Justify your answer. (c) Formulate a least squares problem for this data fitting problem. How is the solution of the least squares problem related to x? Illustrate the idea via a graph. (d) Solve the least squares problem for the approximate (best) solution x. Show also the solution graphically. (e) What is the projection p of the vector b onto the column space of A?